This invention relates to the field of piezoelectric resonators and more particularly to quartz crystal resonators that are highly insensitive to paraxial accelerations.
Frequency perturbations are produced in thickness mode crystal resonators by acceleration-induced forces acting on the body of the resonator. These forces are distributed throughout the resonator volume and vary with the acceleration direction. For specific acceleration directions, the effect can be sharply reduced by changing the points of application of the mounting supports. When the acceleration direction is known in advance, positioning the resonator with respect to the direction minimizes the problem. In high shock and vibration environments, however, accelerations occur in arbitrary directions with ensuing large frequency shifts in the crystal resonance frequency. When the acceleration is arbitrarily oriented with respect to the resonator, no crystal cut or combination of mounting supports can by themselves produce cancellations of the frequency perturbations to the extent required.
In an article entitled, "Crystal Resonators with Increased Immunity to Acceleration Fields" authored by Arthur Ballato and appearing in the IEEE Transactions on Sonics and Ultrasonics, Vol. SU-27, No. 4, July, 1980, pp. 195-201, a comparison is made between conventional and ring-supported plate-type crystal resonators with a showing of the effects of out-of-plane acceleration on each. As stated therein, the conventional resonator is subjected to simply supported boundary conditions at its edges while the ring-supported resonator has double cantilever edge boundary conditions. Since frequency shift is proportional to deformation at the center of the plate, it is shown to be less for a ring-supported structure. Also when the acceleration is in the plane of the plate, one cannot predict the magnitude of the effect of acceleration except that it will depend on the azimuth angle of the acceleration field. The improvement provided by the ring-supported resonator lends itself to crystals of any type of cut, typical examples being the AT cut and the SC cut, which are well known to those skilled in the art. While the above comparison was made with a bi-plano structure, crystal resonators configured as plano-convex or bi-convex forms were noted to be suitable alternatives.